The degradative enzyme that recognizes specific nucleotide sequences and cuts up DNA is called a restriction enzyme or restriction endonuclease.

Here's a breakdown:

* Degradative enzyme: This means it breaks down a molecule, in this case, DNA.

* Recognizes specific nucleotide sequences: Each restriction enzyme has a specific short sequence of DNA it recognizes, usually 4-8 base pairs long. This sequence is called the restriction site.

* Cuts up DNA: When the enzyme finds its restriction site, it cuts the DNA molecule at that point. This cut can be a blunt cut (both strands cut at the same point), or a sticky cut (the ends of the cut DNA strands have overhangs).

Restriction enzymes are essential tools in molecular biology for various reasons, including:

* DNA cloning: Creating recombinant DNA molecules.

* Gene editing: Modifying specific genes in organisms.

* DNA fingerprinting: Identifying individuals based on their unique DNA sequences.

Let me know if you'd like more details on any of these applications!